Research Methods Courses

Institute for Pure & Applied Mathematics (IPAM)

Extending the Reach of Quantum Monte Carlo Methods via Machine Learning

Explore how machine learning enhances quantum Monte Carlo methods for electronic structure modeling, improving force calculations and scaling to larger systems in molecular simulations.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Auxiliary-Field Methods for Quantum Materials - IPAM at UCLA

Overview of auxiliary-field quantum Monte Carlo methods for simulating quantum materials, discussing recent advances in ab initio calculations, including correlated sampling and structural optimization.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Quantum Embedding Methods for Correlated Excited States of Point Defects

Explore quantum embedding methods for correlated excited states of point defects, focusing on case studies and challenges in computational approaches for defect systems in quantum technologies.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Localized-Wave-Function Methods in Quantum Chemistry and Their Extension to Quantum Computers

Explore localized wave-function methods in quantum chemistry, their applications to large systems, and potential extensions to quantum computing algorithms for improved efficiency and accuracy.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Many-Body Perturbation Theory and Green's Function Methods - IPAM at UCLA

Explore Green's functions and many-body perturbation theory in quantum physics, covering Feynman diagrams, self-energy, and applications like GW method and DMFT. Gain insights into mathematical structures and open problems.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Low Rank Tensor Methods in High Dimensional Data Analysis

Explore advanced tensor methods for analyzing high-dimensional data, focusing on recent developments, challenges, and applications in various scientific fields.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

IMSA

Frontiers in Mathematics Lecture Series - Research Talk

Explore Lie theory, groupoids, and algebroids in this advanced mathematics seminar. Discover local integration techniques and their implications for non-integrable Lie algebroids.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

IMSA

Research Seminar - Arc-Connectedness of the Space of 1-Dimensional Commuting Diffeomorphisms

Explore arc-connectedness in 1D commuting diffeomorphisms with Andrés Navas. Gain insights into group actions, community spaces, and rotational concepts in this advanced mathematics seminar.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Aaron Sidford- Introduction to Interior Point Methods for Discrete Optimization, Lecture III

Explore interior point methods for discrete optimization, covering theory, advancements, and applications in maximum flow, bipartite matching, and linear programming.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Aaron Sidford: Introduction to Interior Point Methods for Discrete Optimization, Lecture II

Explore interior point methods for discrete optimization, covering theory, advances, and applications in flow, matching, and linear programming problems.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Marina Iliopoulou- Three Polynomial Methods for Point Counting, Lecture II

Explore three powerful polynomial methods for point counting: Dvir's Kakeya problem solution, Guth-Katz's polynomial partitioning, and the slice rank method for arithmetic progressions.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Marina Iliopoulou - Three Polynomial Methods for Point Counting, Lecture I

Explore three powerful polynomial techniques for point counting: Dvir's method, polynomial partitioning, and slice rank method, with applications in finite fields and geometry.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Deterministic Solution of the Boltzmann Equation - Fast Spectral Methods

Explore fast Fourier spectral methods for solving the Boltzmann equation, addressing computational challenges and showcasing applications in rarefied gas dynamics.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Convergent Semi-Lagrangian Methods for the Monge-Ampère Equation on Unstructured Grids

Explores semi-Lagrangian discretisation of Monge-Ampère operator on P1 finite element spaces, discussing challenges and solutions for numerical methods in solving Monge-Ampère equations, with applications in inverse reflector problems.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 9

Explore advanced asymptotic methods for evaluating infinite sums and recognizing sequence patterns. Learn techniques from standard to unconventional, with practical examples and applications in mathematics.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video